Question

Determine which sequence is an arithmetic sequence.

a)

−10, 5, −52, 54, ...

b)

15, 17,19, 111, ...

c)

3, 6, 12, 24, ...


d)

–7, –3, 1, 5, ...

Answer 1

Option D.

Explanation:

We need to find the arithmetic sequence from the given sequences.

A sequence is called an arithmetic sequence if the difference between any two consecutive terms is constant.c In other words, the sequence has common difference.

In option a,

−10, 5, −52, 54, ...

`d_1=a_2-a_1=5-(-10)=15`

`d_2=a_3-a_2=-52-5=-57`

`d_1\\eq d_2`

This sequence is not an arithmetic sequence.

Similarly,

In option b,

15, 17,19, 111, ...

`d_1=a_2-a_1=17-15=2`

`d_3=a_4-a_3=111-19=92`

`d_1\\eq d_3`

This sequence is not an arithmetic sequence.

In option c,

3, 6, 12, 24, ...

`d_1=a_2-a_1=6-3=3`

`d_2=a_3-a_2=12-6=6`

`d_1\\eq d_2`

This sequence is not an arithmetic sequence.

In option d,

–7, –3, 1, 5, ...

`d_1=a_2-a_1=-3-(-7)=4`

`d_2=a_3-a_2=1-(-3)=4`

`d_3=a_4-a_3=5-1=4`

`d_1=d_2=d_3=4`

This sequence is an arithmetic sequence.

Therefore, the correct option is D.

Answer 2

Explanation:

Short Answer D

A alternates in sign. Every odd positioned entry is minus. No arithmetic progression does that.

B A jump from 19 to 111 after going up by 2s starting with 15 is not an arithmetic progression.

C Each entry is multiplied by 2 to get the next entry after the 3. That is a geometric progression. C is not the answer.

D starts at - 7 and has 4 added to it for each successive entry.